Preheat the oven to 350F. Butter a 13×9 inch baking pan then line it with parchment paper. Then butter the parchment paper. Dust with flour.
Put the pistachios in a food processor and pulse until they are finely ground. Be careful not to pulse so much that they turn into a paste, though. Add the flour, baking powder, cinnamon and salt. Pulse once or twice to mix.
In a mixing cup, combine the milk and the vanilla.
In a large bowl, beat together the sugar and butter until it is pale and fluffy. Add the eggs one at a time, beating well in between each addition.
Add the pistachio flour and milk in batches alternately, beginning and ending with the flour mixture while mixing at low speed. Mix just until combined.
Spread the batter evenly in the prepared cake pan.
Bake in the middle of the preheated oven until a toothpick inserted in the middle comes out clean, about 20 minutes.
Cool in the pan on a cooling rack for 10 minutes, then run a knife around the outside of the cake and invert it on the cooling rack. Remove the paper and transfer to a serving platter.
Serve warm or at room temperature.
